Species with which silver-ground carpet moth (Xanthorhoe montanata) interacts

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is a reference to the pattern, rather than their eating habits.
There are moths that attack fabrics and textiles, but the larvae of this species feed on bedstraws and relatives.
The misapprehension is partly maintained by some unscrupulous pest controllers, who have been known to mislead the unwary into thinking that the name does refer to potentially damaging behaviour.